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This presentation was given at the October 2014 ARM TechCon in Santa Clara, CA.  It provides a detailed description of recent changes to Freescale's sensor fusion offering.
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The Sensor Fusion Toolbox for Android includes a feature illustrating how an air mouse might be implemented on top of the Freescale sensor fusion library.  That tool includes documentation which discusses the algorithm.  That documentation is replicated on the MEMS Industry Group GitHub site.  It's been pointed out that this could use a couple additional diagrams to illustrate the geometry behind the calculations.  For that, please see the attached. BTW, The preview below has been somewhat corrupted by the blogging platform.  I suggest you download the powerpoint file before viewing.
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As requested in a prior posting...
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For those of you who do not have access to Google Play, here is the latest .apk file for the Android version of the Sensor Fusion Toolbox.  This version should trap problems which caused previously reported crashes.  There are no visible changes to the functionality.   IF you have access to Google Play, we recommend that you use that as your default installer, as you can automatically get updates.
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All, We are busily working to integrate Version 7.00 of the sensor fusion library into the Kinetis Expert (KEX) ecosystem.  ETA is early August.  I have attached here a preview copy of the user manual for that release.  This is subject to the usual disclaimers: content subject to change, no liability, yada yada yada.  There are a LOT of changes.    These are documented ad nauseum in the user guide.  I've also added a lot of our old blog content into the user guide, as I keep getting requests for them.  Please take a look and give me your feedback.   FYI, Here is a sample main() for the new fusion, running on FreeRTOS:   /* FreeRTOS kernel includes. */ #include "FreeRTOS.h" #include "task.h" #include "queue.h" #include "timers.h" #include "event_groups.h" // KSDK and ISSDK Headers #include "fsl_debug_console.h"  // KSDK header file for the debug interface #include "board.h"              // KSDK header file to define board configuration #include "pin_mux.h"            // KSDK header file for pin mux initialization functions #include "clock_config.h"       // KSDK header file for clock configuration #include "fsl_port.h"           // KSDK header file for Port I/O control #include "fsl_i2c.h"            // KSDK header file for I2C interfaces #include "Driver_I2C_SDK2.h"    // ISSDK header file for CMSIS I2C Driver #include "fxas21002.h"          // register address and bit field definitions #include "mpl3115.h"            // register address and bit field definitions #include "fxos8700.h"           // register address and bit field definitions // Sensor Fusion Headers #include "sensor_fusion.h"      // top level magCal and sensor fusion interfaces #include "control.h"           // Command/Streaming interface - application specific #include "status.h"            // Sta:tus indicator interface - application specific #include "drivers.h"           // NXP sensor drivers OR customer-supplied drivers // Global data structures SensorFusionGlobals sfg;                ///< This is the primary sensor fusion data structure ControlSubsystem controlSubsystem;      ///< used for serial communications StatusSubsystem statusSubsystem;        ///< provides visual (usually LED) status indicator PhysicalSensor sensors[3];              ///< This implementation uses three physical sensors EventGroupHandle_t event_group = NULL; static void read_task(void *pvParameters);              // FreeRTOS Task definition static void fusion_task(void *pvParameters);            // FreeRTOS Task definition /// This is a FreeRTOS (dual task) implementation of the NXP sensor fusion demo build. int main(void) {     ARM_DRIVER_I2C* I2Cdrv = &I2C_S_DRIVER_BLOCKING;       // defined in the <shield>.h file     BOARD_InitPins();                   // defined in pin_mux.c, initializes pkg pins     BOARD_BootClockRUN();               // defined in clock_config.c, initializes clocks     BOARD_InitDebugConsole();           // defined in board.c, initializes the OpenSDA port     I2Cdrv->Initialize(NULL);                                 // Initialize the KSDK driver for the I2C port     I2Cdrv->Control(ARM_I2C_BUS_SPEED, ARM_I2C_BUS_SPEED_FAST);      // Configure the I2C bus speed     initializeControlPort(&controlSubsystem);                           // configure pins and ports for the control sub-system     initializeStatusSubsystem(&statusSubsystem);                        // configure pins and ports for the status sub-system     initSensorFusionGlobals(&sfg, &statusSubsystem, &controlSubsystem); // Initialize sensor fusion structures     // "install" the sensors we will be using     sfg.installSensor(&sfg, &sensors[0], FXOS8700_I2C_ADDR, 1, (void*) I2Cdrv, FXOS8700_Init,  FXOS8700_Read);     sfg.installSensor(&sfg, &sensors[1], FXAS21002_I2C_ADDR, 1, (void*) I2Cdrv, FXAS21002_Init, FXAS21002_Read);     sfg.installSensor(&sfg, &sensors[2], MPL3115_I2C_ADDR, 2, (void*) I2Cdrv, MPL3115_Init, MPL3115_Read);     sfg.initializeFusionEngine(&sfg);         // This will initialize sensors and magnetic calibration     event_group = xEventGroupCreate();     xTaskCreate(read_task, "READ", configMINIMAL_STACK_SIZE, NULL, tskIDLE_PRIORITY + 2, NULL);     xTaskCreate(fusion_task, "FUSION", configMINIMAL_STACK_SIZE, NULL, tskIDLE_PRIORITY + 1, NULL);     sfg.setStatus(&sfg, NORMAL);                // If we got this far, let's set status state to NORMAL     vTaskStartScheduler();                      // Start the RTOS scheduler     sfg.setStatus(&sfg, HARD_FAULT);            // If we got this far, FreeRTOS does not have enough memory allocated     for (;;) ; } static void read_task(void *pvParameters) {     uint16_t i=0;                       // general counter variable     portTickType lastWakeTime;     const portTickType frequency = 1;   // tick counter runs at the read rate     lastWakeTime = xTaskGetTickCount();     while (1)     {         for (i=1; i<=OVERSAMPLE_RATE; i++) {             vTaskDelayUntil(&lastWakeTime, frequency);             sfg.readSensors(&sfg, i);              // Reads sensors, applies HAL and does averaging (if applicable)         }         xEventGroupSetBits(event_group, B0);     } } static void fusion_task(void *pvParameters) {     uint16_t i=0;  // general counter variable     while (1)     {         xEventGroupWaitBits(event_group,    /* The event group handle. */                             B0,             /* The bit pattern the event group is waiting for. */                             pdTRUE,         /* BIT_0 and BIT_4 will be cleared automatically. */                             pdFALSE,        /* Don't wait for both bits, either bit unblock task. */                             portMAX_DELAY); /* Block indefinitely to wait for the condition to be met. */         sfg.conditionSensorReadings(&sfg);  // magCal is run as part of this         sfg.runFusion(&sfg);                // Run the actual fusion algorithms         sfg.applyPerturbation(&sfg);        // apply debug perturbation (testing only)         sfg.loopcounter++;                  // The loop counter is used to "serialize" mag cal operations         i=i+1;         if (i>=4) {                         // Some status codes include a "blink" feature.  This loop                 i=0;                        // should cycle at least four times for that to operate correctly.                 sfg.updateStatus(&sfg);     // This is where pending status updates are made visible         }         sfg.queueStatus(&sfg, NORMAL);      // assume NORMAL status for next pass through the loop         sfg.pControlSubsystem->stream(&sfg, sUARTOutputBuffer);      // Send stream data to the Sensor Fusion Toolbox     } } /// \endcode
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This is a pre-release .msi installer for the Freescale Sensor Fusion Toolbox for Windows NEXT RELEASE.  This (or a later copy) will eventually replace the release copy at http://www.freescale.com/sensorfusion.  Altough this is a preview copy, it is believed stable.  Please let us know of any issues seen.  This version has a nice feature in that it can re-flash your Freedom board (KL25Z, KL26Z, KL46Z, K20D50M and K64F) with the matching firmware.  The new feature is under the File->Flash menu item.  There have also been some nice changes made to the "Magnetics" view.
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The attached is a PRE-RELEASE copy of the next version of the Freescale Sensor Fusion Library for Kinetis MCUs.  It is a pre-release because we are still working to update the datasheet and userguide to accomodate new changes.  The datasheet and user guides included in this copy are identical to the current production versions found at http://www.freescale.com/sensorfusion.  This is the first release of the library which provides ALL SOURCE CODE.  The software license is unchanged from the prior release, and is re-produced at the end of this posting.  Please do not download the file if you can't agree to these license terms.   In order to get around virus filter on the community, I've had to create a simple zip file of the fusion toolkit.  There's no installer.  Just unzip it in your directory of choice.   Pre-Release Notes for Freescale Sensor Fusion Library for Kinetis MCUs Previous production release: build 417 This release: build 420 This is a pre-release kit.  The included datasheet and user guide relate to the previous version (build 417).  Updates are in progress and will be published shortly. In the meantime, changes (at a high level) are listed below. Changes: 1.  Removed all license checking functions 2.  Fusion and magnetic calibration libraries are now included in source form.    libFusion.a is now gone.  It has been replaced by additional files in the Sources directory.  3.  Added template projects for Kinetis Design Studio 4.  Added KL46Z board support 5.  Community supported at https://community.freescale.com/community/sensors/sensorfusion 6.  The datasheet has been updated with simulated fusion metrics, code sizes and systick counts 7.  "FLASH_EU" target names have been changed to "FLASH" 8.  Changed branding from "Xtrinsic" to "Freescale".  This resulted in project prefixes  being changed from "XSFK_" to "FSFK_". 9.  Removed the Accelerometer + Magnetometer 6-axis Kalman filter (the eCompass implementation  is more efficient) 10. Debug packets are now on by default.  This enables the Sensor Fusion Toolkit for Android to startup with the correct board display on powerup. 11. The following source files have been renamed:     FSL_utils.c/.h are now drivers.c/.h     tasks_func.c/.h are now tasks.c/.h     proj_config.h is now build.h     ProcessorExpert.c is now main.c     baranski_kalman.h is now kalman.h 12. license.h has been removed 13. Added bare metal eCompass implementation for KL46Z (no MQXLite) 14. This version will not include run configurations for all KDS projects. There are too many permutations, and the tools are being regularly updated. Errata: 1.  Newer K64F Freedom boards can utilize several different versions of the OpenSDA interface.  The MBED drivers do not deal properly with flash security and can temporarily "brick" a board.  In order for the download function to work properly, the value of the NV_FSEC portion of the CPU_FLASH_CONFIG_FIELD within file name Generated_Files/CPU_Config.h must have a value of 0xFE.  Processor Expert (which generates this file) does not currently support that value.  You must make the change manually after running Processor Expert. 2.  When compiling for the first time in KDS, the tool may generate the following error message: "writing to APSR without specifying a bitmask".  This is an invalid error. Simply build a second time and the error will disappear. 3.  MQXLite 1.1.0 created via Processor Expert incorrectly handles contexts switches for the  floating point unit on the K64F.  As shipped, this does not present a problem because  floating point computations are normally completed within one sample period.  However if you add additional code to that project template, such that computations extend beyond one sample period, you will get incorrect results (there is no warning!). MQXLite 1.1.1 fixes this issue.  Check the MQX1 settings in Processor Expert to see which  version you are using. 4.  I2C transmission speeds are configured for 300KHz to 400KHz.   During the build process, it is normal to see the following:     "Warning: The device is designed to operate up to 100kHz! (SCL frequency)".     The development team routinely operates at higher I2C frequencies, although these are not necessarily guaranteed in the device datasheets.  Other warnings arise from the  MQXLite code generated by Processor Expert.  The actual fusion library is believed to be clean. Xtrinsic Sensor Fusion Library for Kinetis MCUs License: LA_OPT50 Version 20 January 2014 IMPORTANT. Read the following Freescale Software License Agreement (“Agreement”) completely.  By selecting the “I Agree” button at the end of this page, you indicate that you accept the terms of this Agreement and you also acknowledge that you have the authority, on behalf of your company, to bind your company to such terms.  You may then download or install the file. FREESCALE END-USER SOFTWARE LICENSE AGREEMENT This is a license agreement between you (either as an individual or as an authorized representative acting on behalf of your employer) and Freescale Semiconductor, Inc. (“Freescale”). It concerns your rights to use software package and any accompanying written materials (the “Software”). The Software includes any updates or error corrections or documentation relating to the Software provided to you by Freescale under this License. In consideration for Freescale allowing you to access the Software, you are agreeing to be bound by the terms of this Agreement. If you do not agree to all of the terms of this Agreement, do not download or install the Software. If you change your mind later, stop using the Software and delete all copies of the Software in your possession or control. Any copies of the Software that you have already distributed, where permitted, and do not destroy will continue to be governed by this Agreement. Your prior use will also continue to be governed by this Agreement. 1.         LICENSE GRANT. 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You specifically represent and warrant that you will not use the Software or any derivative work of the Software for High Risk Activities. 13.       CHOICE OF LAW; VENUE; LIMITATIONS.  You agree that the statutes and laws of the United States and the State of Texas, USA, without regard to conflicts of laws principles, will apply to all matters relating to this Agreement or the Software, and you agree that any litigation will be subject to the exclusive jurisdiction of the state or federal courts in Texas, USA.  You agree that regardless of any statute or law to the contrary, any claim or cause of action arising out of or related to this Agreement or the Software must be filed within one (1) year after such claim or cause of action arose or be forever barred. 14.       CONFIDENTIAL INFORMATION.  You must treat the Software as confidential information and you agree to retain the Software in confidence perpetually, with respect to Software in source code form (human readable), or for a period of five (5) years from the date of termination of this Agreement, with respect to all other parts of the Software.  During this period you may not disclose any part of the Software to anyone other than employees who have a need to know of the Software and who have executed written agreements obligating them to protect such Licensed Software to at least the same degree of care as in this Agreement.  You agree to use the same degree of care, but no less than a reasonable degree of care, with the Software as you do with your own confidential information. You may disclose Software to the extent required by a court or under operation of law or order provided that you notify Freescale of such requirement prior to disclosure, which you only disclose information required, and that you allow Freescale the opportunity to object to such court or other legal body requiring such disclosure. 15.       PRODUCT LABELING.  You are not authorized to use any Freescale trademarks, brand names, or logos. 16.       ENTIRE AGREEMENT.  This Agreement constitutes the entire agreement between you and Freescale regarding the subject matter of this Agreement, and supersedes all prior communications, negotiations, understandings, agreements or representations, either written or oral, if any.  This Agreement may only be amended in written form, executed by you and Freescale. 17.       SEVERABILITY.  If any provision of this Agreement is held for any reason to be invalid or unenforceable, then the remaining provisions of this Agreement will be unimpaired and, unless a modification or replacement of the invalid or unenforceable provision is further held to deprive you or Freescale of a material benefit, in which case the Agreement will immediately terminate, the invalid or unenforceable provision will be replaced with a provision that is valid and enforceable and that comes closest to the intention underlying the invalid or unenforceable provision. 18.       NO WAIVER.  The waiver by Freescale of any breach of any provision of this Agreement will not operate or be construed as a waiver of any other or a subsequent breach of the same or a different provision.     © 2004-2014 Freescale Semiconductor, Inc. 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The attached is the windows installer for the latest verson of the Windows version of the Freescale Sensor Fusion Toolbox.  This version must be used with Version 5.00 of the sensor fusion library.  It is NOT backward compatible, as the structure of the undocumented Kalman filter packet has changed. Please uninstall any prior versions of the toolbox before running this installer. As in prior releases, you can reflash your Freedom boards from within the application itself.  So if you want to try the new fusion without downloading the new library and firing up KDS or CodeWarrior, you can. Version 5.00 was posted to this same board just a few minutes ago in a separate post.  It contains full documentation, including algorithm development, datasheet and user guide. Regards, Mike Stanley
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Attached is a PDF dump of a classic blog post.  Please forgive the format problems.  I'll work with the web team in January to get it reposted to the NXP site. Mike
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I am occasionally asked for the source code for the Android version of our Sensor Fusion Toolbox.  Well, here it is, complete with new NXP graphics and updated links.
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All, We've had some problems with migration of Freescale blogs over to the NXP domain.  One set of listings that gets requested a fair bit are the postings on orientation representations.  The attached is a PDF version of the same material which will be contained in the upcoming Sensor Fusion Version 7.00 User Guide.
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You saw it here first! The attached zip file contains full documentation and source code (both CodeWarrior and KDS) for Version 5 of Freescale's Sensor Fusion Library for Kinetis MCUs. The 6 and 9-axis Kalman filters have been rewritten from scratch by fusion expert Mark Pedley.  The new versions have improved dynamic tracking and at-rest stability.  All documentation has been updated, and full implementation details are included.  We continue to use the BSD 3-clause software license, so you are virtually unlimited in how you use the library.   I will note that due to the Kalman filter changes, Mark made some changes to the undocumented Kalman filter packets which are utilized by the Windows Version of the Freescale Sensor Fusion Toolbox.  This breaks compatibility with older versions of the toolbox.  I will be posting a pre-release of the new one immediately after completing this post.  The Android version of the toolbox does not make use of the Kalman filter packet, and should be forward compatible - although an updated version of that is in the works as well.   Structure of the new library is very similar to Version 4.22, which was the previous production version.  There are changes, but I don't expect anyone to have problems adapting existing projects to the new version of the library.  I think you will get improved performance if you do.   Regards, Mike Stanley
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This is a pre-release version of the Sensor Fusion Toolbox for Windows.  It is essentially the same tool you already know and love.  It differs in terms of the binary images that can be downloaded to your development board.  Clicking File->Flash from the toolbar will present you with a set up updated binaries.  These were built using a brand new set of 6- and 9-axis Kalman filter algorithms.  We expect these to consume much less power (2X or 3X) and to have better gyro tracking.  We are soliciting feedback from existing users of the toolkit with regard to performance of the new filters.  We do not expect to formally release until later in Q2, primarily to give the community time to try them and give us feedback.  We are not releasing source just yet, for the same reason.
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Posted here in response to a query by Michael Smorto. Regards, Mike Stanley
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This this shows how to implement the power cycling feature described in Section 4.8, Fusion Standby mode, of the Version 7.00 Sensor Fusion User Guide.  It will power down the gyro when the board is stationary, and also suspend sensor fusion.   Last computed results continue to be sent until new motion is detected.  One nice side effect is that 6-axis yaw drift is almost eliminated.
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The attached is a preview copy of build 422 of the sensor fusion library, which is currently being tested by the Freescale Sensor's team. Please consult the docs/Release_Notes.txt file for changes from build 420, as well as known errata. This version is released under the following license:   Freescale Sensor Fusion Library for Kinetis MCUs IMPORTANT. Read the following Freescale Software License Agreement (“Agreement”) completely.  By downloading this file, you indicate that you accept the terms of this Agreement and you also acknowledge that you have the authority, on behalf of your company, to bind your company to such terms.  You may then download or install the file. FREESCALE END-USER SOFTWARE LICENSE AGREEMENT Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:     * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.     * Redistributions in binary form must reproduce the above copyright  notice, this list of conditions and the following disclaimer in the  documentation and/or other materials provided with the distribution.     * Neither the name of Freescale Semiconductor, Inc. nor the  names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL FREESCALE SEMICONDUCTOR, INC. BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. © 2004-2014 Freescale Semiconductor, Inc. All rights reserved.
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All, This is my personal "cheat sheet" that I use as reference whenever I have to code angular transformations from one frame of reference to another.  There's nothing unique here, it just organizes things in a way that I can find them quickly.  I hope you find it useful. Mike
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Here's a zip file which incorporates the patch I outlined in my previous posting.
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